A204232 Numbers whose binary reversal is prime.

3, 5, 6, 7, 10, 11, 12, 13, 14, 17, 20, 22, 23, 24, 25, 26, 28, 29, 31, 34, 37, 40, 41, 43, 44, 46, 47, 48, 50, 52, 53, 55, 56, 58, 61, 62, 67, 68, 71, 73, 74, 77, 80, 82, 83, 86, 88, 91, 92, 94, 96, 97, 100, 101, 104, 106, 107, 110, 112, 113, 115, 116, 121

Offset: 1

Author

M. F. Hasler, Jan 13 2012

Keywords

• nonn
• base
• easy

Comments

Base-2 analog of A095179.

If k is a term, then 2*k is a term too. - Michel Marcus, Apr 19 2020

Examples

			3, 5 and 7 are in the sequence because their binary reversal, equal to themselves, is prime.
a(3)=6 is in the sequence, because 6=110[2] (written in base 2), whose reversal 011[2]=3 is prime.
a(5)=11 is in the sequence, because 11=1011[2] (written in base 2), whose reversal 1101[2]=13 is prime.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030101, A095179.

Positions of 2's in A227864.

Programs

Mathematica

Select[Range[170], PrimeQ[FromDigits[Reverse[IntegerDigits[#, 2]], 2]] &] (* Alonso del Arte, Jan 13 2012 *)

PARI

for(n=1,1e2,isprime((t=binary(n))*vector(#t,i,1<
				

Python

from sympy import isprime
def ok(n): return isprime(int(bin(n)[2:][::-1], 2))
print(list(filter(ok, range(1, 122)))) # Michael S. Branicky, Sep 06 2021

Python

# alternate program constructing terms directly from primes
from sympy import isprime, primerange
def auptobits(maxbits):
    alst = []
    for p in primerange(3, 1<Michael S. Branicky, Oct 29 2024